US8144833B2 - Planning for adaptive radiotherapy - Google Patents
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- US8144833B2 US8144833B2 US12/763,530 US76353010A US8144833B2 US 8144833 B2 US8144833 B2 US 8144833B2 US 76353010 A US76353010 A US 76353010A US 8144833 B2 US8144833 B2 US 8144833B2
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61N—ELECTROTHERAPY; MAGNETOTHERAPY; RADIATION THERAPY; ULTRASOUND THERAPY
- A61N5/00—Radiation therapy
- A61N5/10—X-ray therapy; Gamma-ray therapy; Particle-irradiation therapy
- A61N5/103—Treatment planning systems
- A61N5/1038—Treatment planning systems taking into account previously administered plans applied to the same patient, i.e. adaptive radiotherapy
Definitions
- the present invention relates to the field of radiation therapy, or radiotherapy, and particularly relates to a method that allows a radiotherapy treatment plan to be updated more easily.
- volumetric images of the patient, and specifically the target region need to be obtained so that a plan for the treatment can be constructed.
- the aim of the treatment plan is to establish how to apply the radiotherapy to the patient so that the target region receives the desired, lethal dose, whilst the surrounding healthy tissue receives as little dose as possible.
- Radiotherapy is often delivered by a linear accelerator-based system, which produces a beam of high-energy x-rays and directs this toward a patient.
- the patient typically lies on a couch or patient support, and the beam is directed toward the patient from an offset location.
- the beam source is rotated around the patient while keeping the beam directed toward the target point (the “isocentre”).
- the result is that the isocentre remains in the beam at all times, but areas immediately around the isocentre are only irradiated briefly by the beam during part of its rotation.
- the dose to the tumour is maximised whilst the dose to surrounding healthy tissue is reduced.
- the cross-section of the beam can be varied by way of a range of types of collimator, such as the so-called “multi-leaf collimator” (MLC) illustrated in EP 0,214,314. These can be adjusted during treatment so as to create a beam whose cross-section varies dynamically as it rotates around the patient.
- MLC multi-leaf collimator
- Radiotherapy apparatus can also be varied during treatment, such as the speed of rotation of the source and the dose rate.
- speed of rotation of the source and the dose rate.
- the volumetric images are therefore analysed to identify a target region into which a minimum dose is to be delivered, any sensitive regions such as functional organs for which a maximum dose must be observed, and other non-target regions into which the dose is to be generally minimised.
- This three-dimensional map must then be used to develop a treatment plan, i.e. a sequence of source movements, collimator movements, and dose rates which result in a three-dimensional dose distribution that (a) meets the requirements as to maximum and minimum doses (etc) and (b) is physically possible, e.g. does not require the source to rotate around the patient faster than it is physically capable.
- courses of radiotherapy are usually fractionated. That is, they usually comprise several cycles of a short period of therapy (known as a fraction) followed by a recovery period.
- Unhealthy tissue i.e. that which is the target of the therapy
- Unhealthy tissue takes longer than healthy tissue to recover from each dose of radiation. Therefore, by managing the therapeutic dose that is delivered in each fraction, as well as the length of the recovery period between each fraction, the unhealthy tissue can gradually be destroyed while the healthy tissue survives.
- the target region will move and/or change shape during the course of the treatment. This can mean that the original treatment plan becomes ineffective, as it was based on a different three-dimensional pattern of regions. The consequence of this is that the target tissue may receive a lower dose than intended and healthy tissue may receive a higher dose than desired.
- new images of the patient and target region can be taken before the start of each fraction, and the treatment plan re-calculated to compensate for any movement of the target region.
- this inter-fraction imaging it is preferable for this inter-fraction imaging to take place with the patient in the same position as they will be in during treatment. To that end, the patient needs to stay in the same position during imaging, during the period while the treatment plan is being updated, and also during the course of the treatment. This can be some time, increasing the potential discomfort of the patient. A reduction in the time taken to complete this process would be beneficial both to the patient and to the facility operating the radiotherapy apparatus, who could then treat more patients than before in the same period of time.
- U.S. Pat. No. 7,593,505 discloses a method in which a library of previously accepted treatment plans is used to speed up creation of a new treatment plan at the start of the planning process.
- European patent EP1238684 discloses a method in which the treatment plan is updated before each fraction by combining new image information with an existing approved plan for the same patient. However, both of these methods still take a relatively long time to compute.
- the present invention seeks to remedy the problems associated with the prior art by providing an improved (i.e. faster) method for updating treatment plans between fractions.
- Treatment plan generation is a predominantly automated process, to reduce the time required. However, even with full automation the process (referred to as 2-phase ⁇ -constraint, or 2p ⁇ c) is still time-consuming. During the initial planning period a number of iterations can be required until the optimum plan is obtained.
- the original dose distribution problem has constraints imposed by the maximum doses receivable by the tissues surrounding the target.
- Lagrangian a function is formed, known as a Lagrangian.
- the different constraints are weighted by “Lagrange multipliers”.
- the Lagrangian is a saddle-shaped function defined by the normal variable (i.e. x) and the Lagrange multipliers (i.e. ⁇ ).
- the optimal solution of this function is the saddle point defined by a unique x (optimal solution for the constrained objective) and ⁇ (the Lagrange multipliers).
- the obtained Lagrange multipliers are generally not important.
- the multi-criteria optimisation is written as a weighted-sum function
- the inventors have realised that the Lagrange multipliers found for the constrained objectives may be used for the weights.
- the optimal solution can be found in only one optimisation instead of many as in the 2p ⁇ c method.
- the Lagrange multipliers found using a first image e.g. a planning scan
- an optimisation method e.g. ⁇ c or 2 p ⁇ c methods
- the Lagrange multipliers can be used as the weights in a weighted-sum function.
- the present invention provides an optimization method of a fluence pattern, to be provided by a radiotherapy apparatus to a patient, wherein a first fluence pattern is calculated based on a first image of a treatment area of the patient and one or more geometric constraints of the radiotherapy apparatus, and wherein generation of the first fluence pattern involves the use of one or more Lagrange multipliers.
- the method comprises the steps of, after a period of treatment, obtaining a second image of the treatment area of the patient; and using the second image and said one or more Lagrange multipliers to generate a second fluence pattern.
- the method may be performed largely by computer, and so a further aspect of the invention provides a computer program product for performing the above method.
- FIG. 1 is a flowchart of a method according to embodiments of the present invention.
- a proposed radiotherapy treatment plan is typically prepared by an automated process. This can then be reviewed by a physician to ensure that it meets the clinical needs of the patient; if necessary the physician can adjust the treatment parameters until an acceptable treatment plan is produced.
- This process uses as one of its inputs a three-dimensional image of the region that will (or may) be irradiated, which has been segmented by manual or automated processes (or some mix of the two) in order to indicate whether a specific part of the image such as a voxel (i.e. a three-dimensional pixel) is either not part of the patient (i.e. free space), part of the tumour or other target to be irradiated, a non-sensitive healthy part of the patient, or a sensitive healthy part of the patient.
- Target regions are allocated a minimum dose that is to be delivered, determined by the clinical outcome that is desired.
- Sensitive regions are allocated a maximum dose that must not be exceeded, else irreparable damage may be caused to the patient.
- Non-sensitive areas such as skin, fat and muscle tissue do not have a specific upper limit but are subject to the general aim of the process which is to minimise the dose to healthy tissue.
- ⁇ -constraint ( ⁇ c) method set out in Haimes Y Y, Lasdon L S and Wismer D A (1971) “ On a bicriterion formulation of the problems of integrated system identification and system optimization ”, IEEE Trans. Man Cybern. 1 296-7.
- a preferred form of this method is known as the 2p- ⁇ c method and is explained in various publications, including Wilkens, J. J., Alaly J. R., Zakarian K., Thorstad W. L. and Deasy J. O., 2007, “ IMRT treatment planning based on prioritizing prescription goals ”, Phys. Med. Biol. 52 1675-92; Jee K-W, McShan D. L. and Fraas B.
- the ⁇ c method uses an image of the patient together with a set of criteria (objectives) in which each objective is optimized separately, and then constrained while optimizing other, lower-prioritized objectives.
- the extension to the ⁇ c method is known as the 2-phase ⁇ -constraint optimization (2p ⁇ c) method.
- an objective may be considered optimized in that it has reached a defined goal (e.g. radiation fluence incident on a sensitive region under a certain threshold value).
- the objective may not be optimal (e.g. the lowest possible radiation fluence incident on the sensitive region), but it is sufficient for the purposes of the radiotherapy treatment. This relaxation of the requirements for one or more objectives may allow other objectives to be better optimized than previously possible.
- plan computation methods require a significant runtime—sometimes of several hours.
- the effect of this in practice is that clinicians often obtain a volume image of the patient, and then prepare a single plan from that image, which is then used for all fractions in the course of treatment.
- the plan must therefore cater for the range of small movements of the target that are to be expected over the fractionated treatment.
- the plan is designed to deliver a dose to a “planning target volume” (PTV), which is the “clinical target volume” (CTV)—i.e. the actual tumour—plus a margin around the tumour to allow for movement.
- PTV planning target volume
- CTV clinical target volume
- Lagrangian optimisation seeks to optimise, for example, the function: f(x) (2)
- ⁇ is a new variable known as the “Lagrange multiplier”.
- Lagrange multiplier we then locate “stationary points” of the Lagrange function, which are the points at which the gradient or slope of the function is zero. This can be done using well-known techniques of differential calculus or computational methods. The result is a fixed value (or values) of x and ⁇ at which the constraints are complied with and f(x) is minimised.
- ⁇ is of academic interest only.
- equation (5) is very similar to the structure of equation (1), i.e. the weighted sum optimisation problem. That approach could not be used between fractions as the repeated efforts to solve it with different possible weights took too long. According to the invention, therefore, we bypass this problem by preparing a first treatment plan using a Lagrange optimisation process, then retaining the Lagrange multipliers obtained in that process and employing them as the weights in a weighted optimisation process. That reduces the time required for the weighted optimisation process to a level that is an acceptable wait time for a patient between scanning and treatment.
- an initial treatment plan can be derived in a known manner, such as an ⁇ c or 2p ⁇ c method. Then, for each subsequent fraction a fresh image can be prepared and a semi-fresh treatment plan derived using a weighted optimisation process that is limited to the use of weights corresponding to the Lagrange multipliers obtained when preparing the initial treatment plan.
- the initial treatment plan can be used for the first fraction that is delivered. Alternatively, if (for example) there is a significant wait between the initial scan and the first fraction, then a fresh scan can be taken before the first fraction and the treatment plan can be re-calculated based on that scan.
- the pattern of scans for a daily fractioned treatment program might be:
- the radiation is delivered by an apparatus having a source of radiation (e.g. a linear accelerator) and a collimator (e.g. a multi-leaf collimator), both of which are mounted on a rotatable gantry.
- a source of radiation e.g. a linear accelerator
- a collimator e.g. a multi-leaf collimator
- a patient support is movable along a translation axis parallel to the rotation axis of the gantry.
- a patient lies on the support while being irradiated by the source.
- the collimator acts on the radiation beam in a plane transverse thereto, to shape and direct the radiation as appropriate.
- the gantry rotates around the patient, to allow the radiation beam to access the patient from different directions.
- the patient support may move along the translation axis, to allow the radiation beam access to different regions of the patient displaced along the translational direction.
- the treatment plan defines (or is interpreted by the radiotherapy system to define) a fluence pattern deliverable to the patient, and actioned by the system defined above.
- the treatment plan may dictate one or more of: the intensity of radiation delivered by the source; the shape and position of the collimator at different locations around the patient; the position and movement of the patient support; and the position and rotational velocity of the gantry.
- FIG. 1 is a flowchart of a method in accordance with embodiments of the present invention.
- markers are implanted into a patient in or around the treatment area.
- Suitable markers are cylindrical gold markers having a cross-sectional area of 1 mm ⁇ 5 mm, although alternative markers may be used.
- the markers do not move relative to the target region during treatment, and so may be used in subsequent images to compensate for interfraction movement of the target region within the patient.
- a planning computed tomography (CT) scan is obtained of the treatment area of the patient.
- the image contains at least a target region for radiotherapy (e.g. a tumour), and may also contain one or more regions that are especially sensitive to radiation (e.g. healthy organs, healthy tissue, etc).
- a target region for radiotherapy e.g. a tumour
- regions that are especially sensitive to radiation e.g. healthy organs, healthy tissue, etc.
- alternative methods may be used to acquire the image, including magnetic resonance imaging for example.
- a treatment plan i.e. a fluence pattern of radiation
- a constraint method e.g. the ⁇ -constraint or 2p ⁇ c methods described below.
- the treatment plan takes into consideration one or more geometric constraints of the radiotherapy system itself.
- geometric constraints may include the maximum intensity of the source, the width of the collimator leaves, the maximum rotation speed of the gantry, etc.
- the calculation of the first treatment plan generates one or more Lagrange multipliers that will be used later in the weighted-sum method. According to embodiments of the invention, therefore, these Lagrange multipliers are stored in a memory for later access.
- the generation of the treatment plan in step 14 may take some considerable time, so it is not generally practical for the patient to remain in situ while the plan is calculated.
- step 16 the patient presents for their first fraction of treatment, and a further CT image is obtained of the treatment area (although again alternative methods may be used to obtain the image).
- step 18 the markers inserted in step 10 are detected and compared with their location in the first image. If necessary, the second image is compensated for interfraction movement of the patient, e.g. translated such that the positions of the markers in the two images are aligned.
- step 20 the second image (compensated for patient motion if necessary) is used in conjunction with the Lagrange multipliers to generate an updated treatment plan.
- the Lagrange multipliers are input as weights in a weighted-sum method to arrive at an acceptable treatment plan far quicker than previously possible. This aspect will be described in greater detail below.
- step 22 the patient is treated according to the second treatment plan, followed by a period of recovery in step 24 .
- the length of the recovery period will of course be set by the medical practitioners in accordance with the requirements of each case; however, common recovery periods are approximately 24 hours.
- most radiotherapy treatment is delivered in a plurality of fractions.
- the method repeats from step 16 onwards, with a new CT scan being taken before each fraction, and the treatment plan being updated in accordance with the present invention.
- Each objective or constraint reflects the dose applied to structures within the treatment area, whether healthy or unhealthy.
- Objectives are denoted by f i , i ⁇ 1, K, n ⁇ , and the constraints by g j , j ⁇ 1, K, m ⁇ .
- the constraints are summarized in a vector g(x), for which each element should be ⁇ 0.
- x represents proposed fluence patterns.
- the objectives are weighted and summed together.
- the optimization problem to be solved becomes minimize w 1 f 1 (x)+w 2 f 2 (x)+K+w n f n (x) subject to g ( x ) ⁇ 0 (6)
- This optimization problem may be solved for varying combinations of weights, building a database of plans.
- the user can search through this database and select the best plan.
- this can take some time to complete, and may require some human interaction to select an appropriate plan.
- the sum of the weights does not necessarily have to be normalized to 1, but this is usually done because it displays the relative weights more clearly.
- the ⁇ -constraint method optimizes one objective at a time while keeping the others constrained. (Similar methods are goal programming and lexicographic ordering.) This method optimizes each objective only once.
- the method may be summarized by minimize f 1 (x) subject to g ( x ) ⁇ 0 where f 1 (x) is the objective with the highest priority.
- f 1 (x) is the objective with the highest priority.
- f 2 (x) is the objective with the second-highest priority. This process is repeated for each successively lower-priority objective until all objectives have been minimized as far as possible, bearing in mind the constrained higher-priority objectives.
- this method may be extended in embodiments of the present invention to a 2-phase ⁇ -constraint optimization (2p ⁇ c), where a goal can be assigned to each objective.
- a goal can be assigned to each objective.
- the parotid is then limited to 26 Gy while minimizing the dose to a lower prioritized organ at risk (OAR) (e.g. the submandibulary gland).
- OAR organ at risk
- a prioritized list which may be called a wish list.
- Each priority contains an objective and a desired goal. So, for n objectives, objective f i (x) has priority i and goal b i .
- the list may contain (hard) constraints g(x) which are to be met at all times.
- the objective having highest priority is optimized: minimize f i (x) subject to g ( x ) ⁇ 0
- the weights for the weighted-sum method may be chosen to be equal to the Lagrange multipliers for the constrained objectives from the last iteration of the E-constraint optimization, as this results in an identical optimal solution.
- ⁇ ⁇ (x*, ⁇ *, ⁇ *) be the Lagrangian for the optimal solution of the final iteration of an ⁇ -constraint optimization (7):
- the constraints g(x) can be assumed to be linear independent.
- the set of Lagrange multipliers ⁇ is unique. Therefore, ⁇ ⁇ *.
- the Lagrangian ⁇ circumflex over ( ⁇ ) ⁇ w is convex in x ( ⁇ and ⁇ are fixed)
- the Lagrange multipliers ⁇ i * calculated during generation of the initial treatment plan using either the ⁇ -constraint method or the 2p ⁇ c method, can be input as the weights w i in the weighted-sum method for updating the treatment plan in later fractions.
- the present invention therefore provides a method for updating and optimizing a treatment plan for radiotherapy.
- An initial plan, calculated using a constraint-driven method may be updated using a weighted-sum method, where Lagrange multipliers generated in the constraint method are reused as the weights in the weighted sum.
- This method results in acceptable updated treatment plans that are generated in a small fraction of the time taken to generate an entirely new treatment plan, reducing patient discomfort and ensuring the radiotherapy facility can treat more patients.
Abstract
Description
w1f1(x)+w2f2(x)+w3f3(x)+ . . . +wnfn(x) (1)
f(x) (2)
g(x)=c (3)
(x, λ)=f(x)+λ(g(x)−c) (4)
(x, λ 1, λ2, . . . , λn)=f(x)+λ1(g(x)−c)+λ2(g(x)−c)+ . . . +λn(g(x)−c) (5)
Day | Scan | Plan | Method | Treatment | ||
1 | Yes | Initial | εc or 2pεc | Yes | ||
2 | Yes | Plan 2 | Weighted sum | Yes | ||
3 | Yes | Plan 3 | Weighted sum | Yes | ||
. . . | . . . | . . . | . . . | . . . | ||
n | Yes | Plan n | Weighted sum | Yes | ||
-
- Alternatively:
Day | Scan | Plan | Method | Treatment | ||
0 | Yes | Initial | εc or 2pεc | No | ||
1 | Yes | Plan 1 | Weighted sum | Yes | ||
2 | Yes | Plan 2 | Weighted sum | Yes | ||
. . . | . . . | . . . | . . . | . . . | ||
n | Yes | Plan n | Weighted sum | Yes | ||
minimize w1f1(x)+w2f2(x)+K+wnfn(x)
subject to g(x)≦0 (6)
minimize f1(x)
subject to g(x)≦0
where f1(x) is the objective with the highest priority. Once minimized, f1(x) is constrained to its minimal value and f2(x) calculated, where f2(x) is the objective with the second-highest priority. This process is repeated for each successively lower-priority objective until all objectives have been minimized as far as possible, bearing in mind the constrained higher-priority objectives.
minimize fi(x)
subject to g(x)≦0
where δ is a slight relaxation to create some space for the subsequent optimizations, set to 1.03 (3%) in one embodiment. Note that this relaxation is not mandatory, but may prevent the optimization algorithm from stalling due to numerical problems. In other embodiments, a relaxation of δ=1+O(10−4) may be used, as this is often enough to prevent numerical problems; however, a relaxation of δ=1.03 also prevents the solution from ending up in one of the end points of the Pareto curve.
minimize f2(x)
subject to g(x)≦0
f 1(x)≦ε1
minimize fi(x)
subject to g(x)≦0
f k(x)≦εk , kε{1,K,n}\i
and then set εi =f i(x*)δ.
minimize fn(x)
subject to g(x)≦0
f i(x)≦εi , iε{1,K,n−1} (7)
-
- Proof.
from Λw does not change the optimal solution. Introduce
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US9925391B2 (en) | 2013-06-21 | 2018-03-27 | Siris Medical, Inc. | Multi-objective radiation therapy selection system and method |
US10293179B2 (en) | 2014-10-31 | 2019-05-21 | Siris Medical, Inc. | Physician directed radiation treatment planning |
US10799716B2 (en) | 2018-10-18 | 2020-10-13 | Varian Medical Systems International Ag | Streamlined, guided on-couch adaptive workflow |
US11648418B2 (en) | 2017-06-22 | 2023-05-16 | Reflexion Medical, Inc. | Systems and methods for biological adaptive radiotherapy |
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US8315357B2 (en) * | 2009-10-08 | 2012-11-20 | The Board Of Trustees Of The Leland Stanford Junior University | Radiation therapy inverse treatment planning using a regularization of sparse segments |
US9091628B2 (en) | 2012-12-21 | 2015-07-28 | L-3 Communications Security And Detection Systems, Inc. | 3D mapping with two orthogonal imaging views |
US10610701B2 (en) | 2013-06-21 | 2020-04-07 | Siris Medical, Inc. | Multi-objective radiation therapy selection system and method |
US10293180B2 (en) | 2013-06-21 | 2019-05-21 | Siris Medical, Inc. | Multi-objective radiation therapy selection system and method |
US9925391B2 (en) | 2013-06-21 | 2018-03-27 | Siris Medical, Inc. | Multi-objective radiation therapy selection system and method |
US10293179B2 (en) | 2014-10-31 | 2019-05-21 | Siris Medical, Inc. | Physician directed radiation treatment planning |
US11020613B2 (en) | 2014-10-31 | 2021-06-01 | Siris Medical, Inc. | Physician directed radiation treatment planning |
US11648418B2 (en) | 2017-06-22 | 2023-05-16 | Reflexion Medical, Inc. | Systems and methods for biological adaptive radiotherapy |
US10799716B2 (en) | 2018-10-18 | 2020-10-13 | Varian Medical Systems International Ag | Streamlined, guided on-couch adaptive workflow |
US11135448B2 (en) | 2018-10-18 | 2021-10-05 | Varian Medical Systems International Ag | Streamlined, guided on-couch adaptive workflow |
US11583700B2 (en) | 2018-10-18 | 2023-02-21 | Siemens Healthineers International Ag | Streamlined, guided on-couch adaptive workflow |
US11865366B2 (en) | 2018-10-18 | 2024-01-09 | Siemens Healthineers International Ag | Streamlined, guided on-couch adaptive workflow |
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